Electronics Manufacturing – B324
Inventory models
Economic order quantity (
EOQ) is the classical inventory model for stock held on cycle with assumptions of
known demand and production lead time. The objective is to select an order quantity that minimizes the marginal annual costs for
holding inventory and
placing orders.
The
annual demand for a product is
2,000. The
unit cost of each product is
£100 and the
storage cost per annum amounts to
20% of stock value.
Each order costs £30 for processing. What is the optimal number of
orders per year?
From the problem description,
A is £30 and
D is 2,000.
H is calculated as a percentage of the unit cost:
£100 x 0.20 = £20
The first step of the EOQ calculation is:
2 x £30 x 2,000 = £120,000
then,
£120,000 ÷ £20 = 6,000
and finally,
the square root of 6,000 is approximately 77
Using 77 as the
Q value, the optimal number of
orders per year is approximately:
2,000 ÷ 77 = 26
On average,
10 products are sold daily and the retailer is open
240 days per year. Each product costs
£50 and the holding cost is
24% of the product cost. There is a cost of
£9 per order. What is the
total annual inventory cost at the optimal inventory level?
From the problem description,
A is
£9
D is calculated from the daily sales:
10 x 240 = 2,400
H is calculated as a percentage of the unit cost:
£50 x 0.24 = £12
The first step of the EOQ calculation is:
2 x £9 x 2,400 = £43,200
then,
£43,200 ÷ £12 = 3,600
and finally,
the square root of 3,600 is 60
Using 60 as the
EOQ value, the
total annual inventory cost is:
60 x £12 = £720
A manufacturer has
20 retailer customers. Each customer orders a
monthly average of 400 products with a
standard deviation of 20 products. The manufacturer has committed to a
99.73% service level agreement for order fulfillment. What is the
comparative efficiency between having
20 warehouses and
5 warehouses?
A service level agreement for
99.73% requires
3 standard deviations of variable inventory for
each warehouse:
400 + ( 3 x 20 ) = 460 products
The base case of
20 warehouses would require the manufacturer to maintain a total monthly inventory level of:
460 x 20 = 9,200 products
The equivalent
standard deviation for a group of
4 retailers being serviced by 1 warehouse (
5 warehouses total) is:
( square root of 4 ) x ( 20 ) = 2 x 20 = 40 products
A service level agreement for
99.73% requires
3 standard deviations of variable inventory for
each warehouse:
( 4 x 400 ) + ( 3 x 40 ) = 1,720 products
The case of
5 warehouses would require the manufacturer to maintain a total monthly inventory level of:
1,720 x 5 = 8,600 products
The
efficiency of variability pooling is calculated as:
( 9,200 - 8,600 ) ÷ 9,200 = 600 ÷ 9,200 = 6.5% efficiency
The
cost to manufacture one product is
£20. The manufacturer sells at a
wholesale price of
£50 and its
retail price is
£100. What is the
buy back price for optimal risk sharing between the manufacturer and the retailer customer?
The
optimal ratio is calculated as:
( 100 - 20 ) ÷ 100 = 80 ÷ 100 = 80%
When the buy back price is
£30, the ratio is low and would cause the retailer to
keep inventory below the optimal quantity:
( 100 - 50 ) ÷ ( 100 - 30 ) = 50 ÷ 70 = 71%
When the buy back price is
£40, the ratio is high and would cause the retailer to
keep inventory above the optimal quantity:
( 100 - 50 ) ÷ ( 100 - 40 ) = 50 ÷ 60 = 83%
When the buy back price is
£35, the ratio is
low, but closer to optimal:
( 100 - 50 ) ÷ ( 100 - 35 ) = 50 ÷ 65 = 77%
When the buy back price is
£37.50, the ratio is
optimal:
( 100 - 50 ) ÷ ( 100 - 37.50 ) = 50 ÷ 62.50 = 80%
Which is the same as using the
formula above:
100 - ( (100 - 50) ÷ 0.8 ) = 100 - ( 50 ÷ 0.8 ) = 100 - 62.50 = 37.50
